To construct asymptotically-Euclidean Einstein’s initial data sets, we introduce the localized seed-to-solution method, which projects from approximate to exact solutions of the Einstein constraints. The method enables us to glue together initial data sets in multiple asymptotically-conical regions, and in particular construct data sets that exhibit the gravity shielding phenomenon, specifically that are localized in a cone and exactly Euclidean outside of it. We achieve optimal shielding in the sense that the metric and extrinsic curvature are controlled at a super-harmonic rate, regardless of how slowly they decay (even beyond the standard Arnowitt–Deser–Misner (ADM) formalism), and the gluing domain can be a collection of arbitrarily narrow nested cones. We also uncover several notions of independent interest: silhouette functions, localized ADM modulator, and relative energy-momentum vector. An axisymmetric example is provided numerically.

中文翻译：

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爱因斯坦引力的最佳屏蔽


为了构造渐近欧几里得爱因斯坦的初始数据集，我们引入了局部种子到解的方法，该方法将爱因斯坦约束的近似解投影到精确解。该方法使我们能够将多个渐近圆锥区域中的初始数据集粘合在一起，特别是构建表现出重力屏蔽现象的数据集，特别是位于圆锥内且在圆锥外精确欧几里德的数据集。我们实现了最佳屏蔽，即度量曲率和外在曲率被控制在超谐波速率下，无论它们衰减的速度有多慢（甚至超出了标准的阿诺伊特-德瑟-米斯纳（ADM）形式主义），并且粘合域可以是任意狭窄的嵌套锥体的集合。我们还揭示了几个独立感兴趣的概念：轮廓函数、局部 ADM 调制器和相对能量动量矢量。以数值方式提供了轴对称示例。